The American version (as well as the book) makes a huge fuss about Mikael Blomkvist not being able to publish the story of his findings that Gottfried and Martin Vanger tortured, raped and killed a lot of women because it was decided to cover everything up for the sake of Harriet Vanger. His problem with this is only that somebody else tells him what he is allowed to publish.

However, it is never explained why Mikael didn't have any moral problems with covering up so many unsolved murder cases. Gottfried's victims were at least found and identified, but Martin claims that he let them disappear so that no attention was raised. This means that a lot of people don't even know what happened to their family members/friends.

Why did Blomkvist (and the other persons that know about the whole story) never express any moral concerns with his actions? After all, he could have easily identified the murderers of dozens of women and he even had proof!

2 Answers
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In the book, when Dirch Frode asks him (on behalf of Henrik Vanger) not to publish his story, Blomkvist specifically notes:

I don’t intend to hang Harriet out to dry, but somebody has to say something about the women who died in Martin’s basement. Dirch, we don’t even know how many women he tortured and slaughtered. Who is going to speak up on their behalf?

Lisbeth notes his dilemma and offers the following compromise:

Martin videotaped his victims. I want you to do your damnedest to identify as many as you can and see to it that their families receive suitable compensation. And then I want the Vanger Corporation to donate 2 million kronor annually and in perpetuity to the National Organisation for Women’s Crisis Centres and Girls’ Crisis Centres in Sweden.

Therefore, Blomkvist did express concerns over the morality of his actions and was reluctantly mollified by Salander's compromise.

I'm not sure if this made it into the English film adaptation. But I do vaguely recall a scene along these lines in the Swedish flick.

I think it would have become more of a moral question if the culprits were still alive and out in the open. Blomkvist did not reveal these facts because that would attract stigma for the whole Vanger family. Also if things were dug up, the fact that Gottfried and Martin abused their own daughter & sister respectively, would become public knowledge. This could also have affected family business.

Also in my opinion Harriet Vanger had had enough and it was better for her that these things were buried. So Blomkvist suppressed his moral concerns to protect Henrik Vanger & Harriet Vanger.